Abstract [en]

We investigate a new approach for local enhancement of mode superpositions, which builds on the concept of submodeling. To this end, we impose a multiscale split on the reduced solution into a global part defined by the mode superposition method and a local part defined by a patch problem solved in a subspace of the finite element space associated with a subdomain around some region of interest. The patch problem yields a local correction on the modal approximation. We describe the basics of this approach and evaluate the accuracy of the approximation in elastostatic numerical examples. We also demonstrate how the submodeling technique may be applied as a post-processing operation on a set of reduced solutions, for example, from dynamics simulation, to enhance accuracy in some domain of interest. Copyright (C) 2012 John Wiley & Sons, Ltd.

Abstract [en]

Component mode synthesis (CMS) is a classical method for the reduction of large-scale finite element models in linear elasticity. In this paper we develop a methodology for adaptive refinement of CMS models. The methodology is based on a posteriori error estimates that determine to what degree each CMS subspace influence the error in the reduced solution. We consider a static model problem and prove a posteriori error estimates for the error in a linear goal quantity as well as in the energy and L2 norms. Automatic control of the error in the reduced solution is accomplished through an adaptive algorithm that determines suitable dimensions of each CMS subspace. The results are demonstrated in numerical examples.

Abstract [en]

We develop a posteriori error estimates for the error associated with model reduction of elliptic eigenvalue problems using component mode synthesis (CMS). The estimates reflect to what degree each CMS subspace influence the overall error in the reduced solution. This allows for automatic error control through adaptive algorithms that determine suitable dimensions of each CMS subspace.

Abstract [en]

In this paper, we derive a discrete a posteriori error estimate for a thermoelastic model problem discretized using a reduced finite element method. The problem is one-way coupled in the sense that heat transfer affects elastic deformation but not vice versa. A reduced model is constructed using component mode synthesis in each of the heat transfer and linear elastic finite element solvers. The error estimate bounds the difference between the reduced and the standard finite element solution in terms of discrete residuals and corresponding dual weights. A main feature with the estimate is that it automatically gives a quantitative measure of the propagation of error between the solvers with respect to a certain computational goal. The analytical results are accompanied by a numerical example.